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2 years ago

Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a?

Mathematics

1 answer:

trasher [3.6K]2 years ago

7 0

The value of the a in the quadratic equation is 4.

According to the statement

we have given that the x = 1 and the given equation is (2x)^2=a

And we have to find the value of A here.

So, For this purpose, we know that the

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

And the given quadratic equation is

(2x)^2 = a

we know that the x = 1 and put the value of x in it then

(2(1))^2= a

(2)^2= a

a = 4.

Now for rechecking of the value, put a = 4 in the given equation then

(2x)^2 = a

Put a = 4

Then

(2x)^2 = 4

2x = 2

And the value of x become

x = 1.

Which equal to the given value of the x which is 1.

So, The value of the a in the quadratic equation is 4.

Learn more about Quadratic equation here

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Wen is factoring the polynomial, which has four terms. 6x3 – 12x2 7x – 14 6x2 (x – 2) 7(x – 2) Which is the completely factored

-Dominant- [34]

The completely factored form of the Wen's polynomial, which has the four terms initial, is,

$(6x^2+7)(x-2)$

<h3>What is the factor of polynomial?</h3>

The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.

Wen is factoring the polynomial, which has four terms.

$6x^3 - 12x^2+ 7x - 14$ '

Take out the greatest common factor from the equation and make separate groups as,

$6x^2(x - 2)+ 7(x - 2)\\(x-2)(6x^2+7)$

Rearrange the above equation as,

$(6x^2+7)(x-2)$

Thus, the completely factored form of the Wen's polynomial, which has the four terms initial, is,

$(6x^2+7)(x-2)$

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1 year ago

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On

uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

$h(x)=ax(x-7)$ ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

$4=a(3)((3)-7)$

$4=a(3)(-4)$

$\dfrac{4}{(3)(-4)}=a$

$-\dfrac{1}{3}=a$

Putting $a=-\dfrac{1}{3}$ , we get

$h(x)=-\dfrac{1}{3}x(x-7)$ ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

$h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)$